On the influence of pore connectivity on performance of membrane filters

Gu, Binan; Renaud, Dylan; Sanaei, Pejman; Kondic, Lou; Cummings, L. J.

doi:10.1017/jfm.2020.520

Cited by 12 publications

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References 32 publications

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“…We use a continuum model for the particle (foulant) concentration within the feed. To characterize particle transport on a network, we must describe the transport on each edge, accomplished via an advection equation with an adsorptive sink [18,11], then impose conservation of particle flux at each vertex. For each edge e ij = (v i , v j ) of length A ij , with Y a local coordinate measuring distance along the edge from v i , let C ij (Y, T ) be the particle concentration at any point of the edge at time T , then…”

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confidence: 99%

“…Classical models of particle advective transport on graphs were developed and studied by Chapman & Mesbahi [4], but these authors did not incorporate a sink term to capture external effects such as fouling. Meanwhile, Gu et al [11] considered a coarse discretization of a transport equation with deposition on regular layered pore structures with interconnections, which can be generalised to more complex networks (represented by graphs). In this work, we combine these two approaches and formulate a transport equation on the network using the graph theoretical framework.…”

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A Graphical Representation of Membrane Filtration

Gu¹,

Kondic²,

Cummings³

2021

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We analyze the performance of membrane filters represented by pore networks using two criteria: 1) total volumetric throughput of filtrate over the filter lifetime and 2) accumulated foulant concentration in the filtrate. We first formulate the governing equations of fluid flow on a general network, and we model transport and adsorption of particles (foulants) within the network by imposing an advection equation with a sink term on each pore (edge) as well as conservation of fluid and foulant volumetric flow rates at each pore junction (network vertex). Such a setup yields a system of partial differential equations on the network. We study the influence of three geometric network parameters on filter performance: 1) average number of neighbors of each vertex; 2) initial total void volume of the pore network; and 3) tortuosity of the network. We find that total volumetric throughput depends more strongly on the initial void volume than on average number of neighbors. Tortuosity, however, turns out to be a universal parameter, leading to almost perfect collapse of all results for a variety of different network architectures. In particular, the accumulated foulant concentration in the filtrate shows an exponential decay as tortuosity increases.

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confidence: 99%

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confidence: 99%